Proximity-magnetized quantum spin Hall insulator: monolayer 1 T’ WTe2/Cr2Ge2Te6

Van der Waals heterostructures offer great versatility to tailor unique interactions at the atomically flat interfaces between dissimilar layered materials and induce novel physical phenomena. By bringing monolayer 1 T’ WTe2, a two-dimensional quantum spin Hall insulator, and few-layer Cr2Ge2Te6, an insulating ferromagnet, into close proximity in an heterostructure, we introduce a ferromagnetic order in the former via the interfacial exchange interaction. The ferromagnetism in WTe2 manifests in the anomalous Nernst effect, anomalous Hall effect as well as anisotropic magnetoresistance effect. Using local electrodes, we identify separate transport contributions from the metallic edge and insulating bulk. When driven by an AC current, the second harmonic voltage responses closely resemble the anomalous Nernst responses to AC temperature gradient generated by nonlocal heater, which appear as nonreciprocal signals with respect to the induced magnetization orientation. Our results from different electrodes reveal spin-polarized edge states in the magnetized quantum spin Hall insulator.


Optical characterization of monolayer (ML) WTe2 and optical images of ML-
We exfoliate ML WTe2 flakes in a glove box and identify them based on the optical contrast and color. Figs. S1a and S1b show the bright-field and dark-field optical images, respectively. It is clear that the freshly exfoliated ML WTe2 flake is very clean with no visible particles on top. We characterize ML WTe2 flakes using Raman (as shown in Fig. S1c). Two peaks located at 162.1 cm -1 and 214.2 cm -1 are identified as Raman mode 1 5 and 1 2 , respectively, which is consistent with the reported characteristic Raman spectrum of ML WTe2 (1). Here we also show the optical images of ML-WTe2/CGT devices D1 and D7 after the fabrication is complete (as presented in Figs. S1d and S1e). The fabrication details are summarized in the Methods section.

Induced anomalous Nernst effect (ANE) vs. spin Seebeck effect (SSE)
In well-studied ferromagnetic insulator (FMI)/heavy metal (HM) heterostructures, there has been a vigorous debate about the origin of the transverse voltage response to a temperature gradient. Two possible mechanisms can give rise to such a magneto-thermoelectric voltage hysteresis: Anomalous Nernst effect (ANE) due to induced ferromagnetism in HM as a result of the proximity effect and spin Seebeck effect (SSE) which does not require any induced ferromagnetism in HM. It is usually very difficult to exclude either one. In general, SSE voltage is generated by spin-charge conversion in the HM layer with strong spin-orbit coupling (SOC) (1) capable of producing the inverse spin Hall effect (ISHE) signal (3,4 Fig. 1d are consistent with the ANE mechanism in the presence of an in-plane temperature gradient generated by the nonlocal heater. To further confirm the thermoelectric nature of ANE signal in Fig. 1d, we perform heating-power dependence of the ANE signals from channels 3-8, 4-7 and 4-5 of device D1.

Heating-power dependence of ANE signal
Under fixed system temperature, the sample temperature rises due to Joule heat from nonlocal heater. To obtain the heating-power dependence of ANE signal at a fixed sample temperature, we adjust the system temperature accordingly to maintain the targeted sample temperature (Ts=26.5 K) monitored by the sample resistance. As summarized in Fig. S2, the hysteresis loops from channel 3-8(

Experimentally measured and COMSOL simulated temperature difference in ANE device
is an important parameter that determines the value of transverse Seebeck coefficient ) , where is the transverse voltage, i.e., the ANE voltage, generated by a temperature gradient along the x-or longitudinal-direction, is the channel length in the transverse direction. Here we demonstrate that can be determined using both experimental method and finite element simulations.
Experimentally we use the resistance of heater and ML-WTe2 to calibrate the actual temperatures at their respective locations. The resistances as a function of temperature are measured with a very low current density first, which serves as a temperature calibration curve.
As the heater is turned on, local temperatures rise above the system temperature, which can be accurately monitored by the resistance. We use this resistive thermometry to determine the actual temperatures of the heater and ML-WTe2. The heater temperature, as well as the temperature of ML-WTe2, increase as the heating power P increases (as shown in the right panel of Fig. S3a), the actual temperature of the heater (and ML-WTe2) is determined using the R vs. T calibration curve (left-panel of Fig. S3a). In our measurements of P-dependent ANE voltages (as shown in Fig. S2), the actual sample (ML-WTe2) temperature is held at =26.5 K which is monitored by its resistance while adjusting the measurement system temperature. At the constant , the temperature gradient at the sample location is different for different heating power levels. This effect can be seen in the temperature difference between the heater ℎ and for different P's and their linear relation in Fig. S3b. Fig. S3c shows that the -normalized ANE voltages measured in three channels are nearly constant, which is consistent with Fig. S3b. For , assuming a linear temperature decay between the heater and sample, we use In actual devices, the local temperature near the heater is not a linear function of the distance; therefore, we use a finite element method (COMSOL) to simulate the temperature profile in our ANE device. Based on the device configuration (Fig. S3d) ) assuming a linear temperature distribution. Therefore, we greatly underestimate the value of by assuming a linear temperature distribution, and the actual should be one order of magnitude greater than the value determined from the experimentally measured local temperatures assuming a linear temperature profile.

Hz-dependent ANE signals from channels 4-7 and 4-5 at various temperatures
To investigate correlation between the observed ANE signals and ferromagnetic order in CGT layer, we carry out detailed temperature-dependent measurements. Figure 1e summarizes the ANE signal from channel 3-8 at various sample-temperatures ranging from 14.9 K to 67.4 K.

as a function of
Hz at the same selected temperatures. We can clearly see that the characteristics from both channels are similar: the size of the hysteresis loop shrinks as the sample warms up, and the hysteresis loop vanishes above the Curie temperature of the CGT crystal (Tc=61 K), which is also summarized in Fig. 1f. These features strongly suggest that the ANE voltage of ML-WTe2 stems from the proximity-induced ferromagnetism by the adjacent ferromagnetic insulator CGT.

Fig. S4. a, b, Hz-dependent ANE signals from 4-7 (a) and 4-5 (b) channels at various sample
temperatures ranging from 14.9 K to 67.4 K. All the ANE voltages are normalized to heatingpower, sample temperature is calibrated using resistance versus temperature curve.

Anisotropic magnetoresistance (AMR) vs. spin Hall magnetoresistance (SMR)
In FMI/HM heterostructures such as YIG/Pt, there has been a long-standing debate on the origin of observed magnetoresistance and AHE. In ferromagnetic metals, the resistance depends on the relative orientation between the current and magnetization. This is widely known as the decrease from its saturation value as M is aligned with the z(-z) direction. This is obviously contradictory to the peak feature in our 1 MR signal. Hence, the 1f MR signal is clearly the AMR effect expected for the magnetized ML-WTe2. In addition, the 1f AHE signal, i.e., the field-antisymmetric component, provides another proof of the induced ferromagnetism in ML-WTe2. Similar proximity-induced AHE has also been observed in other quantum materials including graphene (24) and topological insulators (25, 26).

Activation energy extracted from the Bulk-only channel of ML-WTe2
As shown in Fig. S5, the conductance of the Bulk-only channel (5-6) is much smaller than that of the Bulk+ Edge channel (13)(14), indicating that the edge channel starts to dominate the transport properties at low temperatures. The conductance of ML-WTe2 increases as the device is warmed up, indicating an energy gap and activated transport properties. We extract the activation energy , or energy gap, through the Arrhenius fit of the form ∝  We adopt a WTe2/CGT bilayer structure to simulate the magnetic proximity effect. A rectangular shaped supercell includes 2×1 unit-cell WTe2 (see Fig. S6). The atomic structure optimization is fully performed. Based on the stacked bilayer structure, we perform DFT calculations following the framework of the generalized gradient approximation (28)     . At 4 K, the 4−7 2 (0 ) signal comes from the edge conduction as previously discussed.
As Vg is swept to large values on both sides, the Fermi level approaches the bulk bands, and more bulk carriers are involved in the transport. In order to fully understand the detailed Vgdependence, the Berry curvature of the electronic band need to be calculated, and AHE conductivity, as well as ANE coefficient, need to be studied.

Separation of bulk and edge ANE signals
The low-temperature ANE signal sign reversal in the Bulk+Edge channel (Fig. 3d) and the absence of the sign reversal in the Bulk-only channel (Fig. 3e) Fig. 4b.

Effect of low-temperature thermal conductivity on ANE magnitude
The P-normalized ANE signals from channels 5-6 and 13-14 in device D7 become significantly larger at low temperatures, a trend contradictory to the third law of thermodynamics.
We attribute this apparent increase in both channels to a rapidly decreasing thermal conductivity at low temperatures, which greatly enlarges the actual since ∝ . Larger in turn leads to an enhanced ANE voltage.
The thermoelectric coefficients S are defined by = , where E is the electrical field produced by the temperature gradient and S the thermoelectric tensor. To understand how thermoelectric transport behaves, it is appropriate to taking thermal conductivity into the account. . As shown in Fig. S11, we find that both curves approach zero as Ts → 0 after they are multiplied by Ts 3 , which is consistent with the expectation from the thermodynamic third law. Above all, we have explained the diverging trend of the ∆ at low temperatures by considering the effect of the vanishing low-temperature thermal conductivity. S11. Replot of the low-temperature ANE signals. The 3 temperature dependence of the phonon thermal conductivity is considered for low temperatures by multiplying the anomalous Nernst effect (ANE) signals from Bulk+ Edge channel (13)(14) and Bulk-only channel (5-6) by